The peak versus off-peak forecasting of intra-day residential loads is a well-studied problem in conventional electricity grids, where the intra-day prices are either fixed at a constant value, or are allowed to change based on a specific time-of-day (TOD) pattern that is however unchanged from day to day irrespective of the actual prevailing level for the daily electricity demand. Such pricing schemes ignore the true cost of supplying electricity, which, particularly during the peak time periods, may often have to be procured by the supplier at a significantly higher cost, e.g., by turning on a local generator or purchasing from the spot market, to satisfy peak demand. To provide an alternative to the intra-day energy management using the traditional voltage control approach, utility companies may also consider providing dynamic incentives to encourage residential customers to schedule their day-ahead TOD usage based on the projected or actual cost of the electricity supply.
The proactive management of the intra-day usage in this manner requires short-term forecasts for the residential electricity usage. Various methods for intra-day load control have also been considered in the past, while not specifically based on the direct use of dynamic pricing context. For example, the curtailing of appliance usage based on dynamic load conditions, optimally matching a plurality of supply options with static forecasts of demands in a micro-grid, as well as price-driven experimental approaches that provide the customer with a measure of the actual cost of electricity. Furthermore, prior approaches for short-term forecasting have typically neglected the intra-day substitutability of residential usage that can occur due to dynamic pricing, even though for example, customer choice models like the Multinomial Logit (MNL) and Probit models have been widely used in other contexts, e.g. for calculating substitutive cross-product price elasticity of sales within consumer product assortments and for developing pricing optimization models for retail category management.
The MNL model has a few well-known limitations that in certain cases may adversely affect the quality of the prediction. First, the MNL model cannot account for any complementary customer-choice alternatives, and it therefore ignores the possibility that the increase in consumption during one period can be positively correlated with the increase in usage for another time period. Second, the assumption of usage substitutability across the day requires the model to compensate for unsatisfied morning demand by a corresponding increase in evening usage. In practice, complementary demand effects are more pronounced in the case of industrial loads where production-runs that contribute a significant portion of daily usage overlap across several time periods, and the latter restriction can be remedied by adopting a nested Logit approach that partitions A.M and P.M loads.